The art is replete with suggestions for attaching blocks or liners by magnets to the ferrous metal jaw or clamping surfaces of clamps and vises and the like to provide a more pliable clamping surface against the workpiece than the hard clamping surfaces and thereby prevent surface damage to the workpiece. Exemplary of such proposals are the structures described in U.S. Pat. Nos. 2,606,470; 2,666,352; 3,065,960; 3,502,318; 3,811,668; and 4,569,511, and in German Patent No. 2,154,287, EPO Patent 0141893 and in the article appearing in American Machinist, "Magnets Hold Wooden Vise-Jaw Liners," July 14, 1958, p. 118. Some of these proposals require modification of the jaw or clamping surfaces to receive magnetic holding elements; others, fittings over the clamping surface edges; and still others require special attaching techniques to the blocks. All appear limited, however, to a fixed and predetermined single position of magnetic attachment of the block or liner to the clamping surface, with no or little possible adjustment of the location of such region, and also lack the facility to vary at will the workpiece supporting dimensions of the block or liner extending beyond or outside the clamping surfaces--and certainly not without separation of the magnetic holding between the block or liner and clamping surface--such as to adapt continually to support different surface configurations, shapes and portions of the workpiece-to-be-clamped.